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LEAVING CERTIFICATE EXAMINATION 2003: PHYSICS – HIGHER LEVEL
2003 Question 1
In an experiment to verify Boyle’s law, a student measured the volume V of a gas at different values of the pressure p.
The mass of the gas was not allowed to change and its temperature was kept constant.
The table shows the data recorded by the student.
p/ kPa 120 180 220 280 320 380 440
V/cm3 9.0 6.0 5.0 4.0 3.5 3.0 2.5
(i) Describe with the aid of a diagram how the student obtained this data.
See diagram.
Note the pressure of the gas from the pressure-gauge and the volume from
the graduated scale.
Turn the screw to decrease the volume and increase the pressure.
Note the new readings and repeat to get about seven readings.
(ii) Draw a suitable graph on graph paper to show the relationship between
the pressure of the gas and its volume.
p/ kPa
120
180
220
280
320
380
440
3
1/V/cm- 0.111 0.167 0.200 0.250 0.286 0.333 0.400
Axes labelled
6 points plotted correctly
Straight line
Good fit
(iii) Explain how your graph verifies Boyle’s law.
A straight line through the origin verifies that pressure is inversely proportional to volume
(iv) Describe how the student ensured that the temperature of the gas was kept constant.
Release the gas pressure slowly, allow time between readings.
2003 Question 2
In an experiment to measure the specific latent heat of vaporisation of water, cold water was placed in a copper
calorimeter.
Steam was passed into the cold water until a suitable rise in temperature was achieved.
The following results were obtained.
Mass of the calorimeter........................... = 73.4 g
Mass of cold water .................................. = 67.5 g
Initial temperature of water..................... = 10 °C
Temperature of the steam........................ = 100 °C
Mass of steam added ............................... = 1.1 g
Final temperature of water ...................... = 19 °C
(i) Describe how the mass of the steam was found.
Final mass of (calorimeter + water + condensed steam) – Initial mass of (calorimeter + water)
(ii) Using the data, calculate a value for the specific latent heat of vaporisation of water.
(ml) steam
+ (mc∆ϑ) steam = (mc∆ϑ) water + (mc∆ϑ) cal
∆ϑwater = 90C, ∆ϑcal= 90C
∆ϑ) steam = 810C
Answer = 2.2 × 106 J kg-1
(iii) Why is the rise in temperature the least accurate value?
Read only to one significant figure {the concept of significant figures is not on the syllabus and shouldn’t
have got asked. It hasn’t appeared since.]
(iv) Give two ways of improving the accuracy of this value.
Use a digital thermometer, use more steam, use less water, insulation, cover, stirring, steam trap
2003 Question 3
The following is part of a student’s report of an experiment to measure the focal length of a converging lens.
“I found the approximate focal length of the lens to be 15 cm.
I then placed an object at different positions in front of the lens so that a real image was formed in each case.”
The table shows the measurements recorded by the student for the object distance u and the image distance v.
u/cm 20.0 25.0 35.0 45.0
v/cm 66.4 40.6 27.6 23.2
(i) How did the student find an approximate value for the focal length of the lens?
Focus the image of a distant object on a screen.
The distance from the lens to screen corresponds to the focal length.
(ii) Describe, with the aid of a labelled diagram, how the student found the
position of the image.
Set up as shown.
Adjust the position of the screen until a sharp image is seen.
(iii) Using the data in the table, find an average value for the focal length of the lens.
(iv) 1/u+ 1/v = 1/f
u/cm 20.0 25.0 35.0 45.0
Average = 15.4 cm
v/cm 66.4 40.6 27.6 23.2
f/cm 15.4 15.5 15.4 15.3
(v) Give two sources of error in measuring the image distance and state how one of these errors can be
reduced.
Image not sharp / parallax error in reading distance / not measuring to centre of lens / zero error in metre stick
4
In an experiment to verify Joule’s law, a heating coil was placed in a fixed mass of water.
The temperature rise Δθ produced for different values of the current I passed through the coil was recorded.
In each case the current was allowed to flow for a fixed length of time.
The table shows the recorded data.
I /A
1.5 2.0 2.5 3.0 3.5 4.0 4.5
Δθ / °C 3.5 7.0 10.8 15.0 21.2 27.5 33.0
(i) Describe, with the aid of a labelled diagram, how the apparatus was arranged in this experiment.
See diagram below.
(ii) Using the given data, draw a suitable graph on graph paper and explain how your graph verifies Joule’s law.
I /A
1.5 2.0 2.5 3.0 3.5
4.0 4.5
Δθ / °C 3.5 7.0 10.8 15.0 21.2 27.5 33.0
I2 /A2
2.25 4.0 6.25 9.0 12.25 16.0 20.25
Label axes
At least 6 correct points
Straight line
Good fit
A straight line through origin shows that ∆ϑ ∝ I2 which verifies Joule’s
Law.
(iii) Explain why the current was allowed to flow for a fixed length of time in each case.
You can only investigate the relationship between two variables at a time and time is a third variable.
(iv) Apart from using insulation, give one other way of reducing heat losses in the experiment.
Start with cold water, change the water for each run, use a lid, shorter time interval, polish calorimeter
5
(a) Stat Hooke’s law.
Hooke’s Law states that when an object is stretched the restoring force is directly proportional to the
displacement, provided the elastic limit is not exceeded.
(b) What is the relationship between the acceleration due to gravity g and the distance from the centre of the
earth?
g is proportional to 1/d2
(c) The diagram shows forces of 5 N applied to a water tap. Calculate the moment of the
couple (torque) on the tap.
Moment = force by distance = 0.3 N m
(d) Which wave phenomenon can be used to distinguish between transverse waves and
longitudinal waves?
Polarisation
(e) Sound intensity level can be measured in dB or dB(A).
What is the difference between the two scales?
The dB(A) is adjusted so that it is suitable for the human ear.
(f) Calculate the critical angle for diamond. The refractive index of diamond is 2.4.
n = 1/ sin c c24.60
(g) What is the purpose of a miniature circuit breaker (MCB) in an electric circuit?
It behaves as a fuse when too large a current flows
(h) What is the photoelectric effect?
It is the emission of electrons from the surface of a hot metal due to radiation of a suitable frequency shining on it.
(i) What is meant by nuclear fusion?
Nuclear fusion is the combining of two small nuclei to form one large nucleus with the release of energy.
(j) Give one contribution made to Physics by either Paul Dirac or Nicholas Callan.
Dirac predicted antimatter.
2003 Question 6
(i) Give the difference between vector quantities and scalar quantities and give one example of each.
A vector has both magnitude and direction whereas a scalar has magnitude only.
(ii) Describe an experiment to find the resultant of two vectors.
1. Attach three Newton Balances to a knot in a piece of thread.
2. Adjust the size and direction of the three forces until the
knot in the thread remains at rest.
3. Read the forces and note the angles.
4. The resultant of any two of the forces can now be shown to be
equal to the magnitude and direction of the third force.
(iii) A cyclist travels from A to B along the arc of a circle of radius 25 m as shown.
Calculate the distance travelled by the cyclist.
The displacement is equivalent to one quarter of the circumference of a circle = 2πr/4 = 25π/2
= 12.5π = 39.3 m.
(iv) Calculate the displacement undergone by the cyclist.
Using Pythagoras: x2 = 252 + 252
 x = 35.3 m. Direction is NW
(v) A person in a wheelchair is moving up a ramp at a constant speed. Their total weight is 900 N.
The ramp makes an angle of 10o with the horizontal.
Calculate the force required to keep the wheelchair moving at a
constant speed up the ramp. (You may ignore the effects of friction.)
If the wheelchair is moving at constant speed then the force up must equal the
force down. So to calculate the size of the force up, we just need to calculate the force down:
F = mgSinϑ
= 900 Sin 10o
= 156.3 N
(vi) The ramp is 5 m long. Calculate the power exerted by the person in the wheelchair if it takes her 10 s to
travel up the ramp.
Power = work/time
Work = Force × displacement = 156.3 × 5 = 780 J
Power = 780/10 = 78 W
7
(i) Describe an experiment to show that sound is a wave motion.
1. Walking slowly from X to Y, you will notice the loudness of the sound increasing
and decreasing at regular intervals.
2. This is because sound waves from the two speakers will interfere both
constructively and destructively, along the path XY.
(ii) What is the Doppler Effect?
The Doppler Effect is the apparent change in the frequency of a wave due to the relative motion between the
source of the wave and the observer.
(iii) Explain, with the aid of labelled diagrams, how this phenomenon occurs.
Non concentric circles, stated or implied as waves
Close parts of circles show high frequency / short wavelength
Centres show direction of movement of source
(iv) Bats use high frequency waves to detect obstacles. A bat emits a wave of frequency 68 kHz and wavelength
5.0 mm towards the wall of a cave. It detects the reflected wave 20 ms later.
Calculate the speed of the wave.
v = fλ
340 m s-1
(v) Calculate the distance of the bat from the wall.
v = s/t
 vt = s = 6.8 m.
Divide by two to get the distance going one way only = 3.4 m.
(vi) If the frequency of the reflected wave is 70 kHz, what is the speed of the bat towards the wall?
f ' = fc / c± u
70000 = (68000)(340)/340 - u
u = 9.7 m s-1
(vii)
Give two other applications of the Doppler Effect.
Speed traps , speed of stars (red shift), landing aircraft, ultrasound (blood movement or heartbeat of foetus), weather
forecasting.
8
(i) Define the unit of current, i.e. the ampere.
The ampere is the amount of charge which, if flowing in two very long parallel wires one metre apart in a vacuum
will experience a force of 2 x 10-7 N per metre length.
(ii) Describe an experiment to demonstrate the principle on which the definition of the ampere is based.
A circuit containing aluminium foil and parallel strips.
When the current is switched on the foil moves.
Various materials conduct electricity.
(iii) Draw a graph to show the relationship between current and voltage for a metal at constant temperature
(iv) Draw a graph to show the relationship between current and voltage for an ionic solution with inactive
electrodes
Axes and straight line starting at v > 0
(v) Draw a graph to show the relationship between current and voltage for a gas.
Axes, curve and plateau
(vi) How would the graph for the metal differ if its temperature were increasing?
If temperature was increasing it would no longer be linear; instead there would be a curve to the right because resistance
would increase.
(vii)
How would the graph for the ionic solution differ if its concentration were reduced?
The slope of the graph would be less (the resistance increases) due to less ions (charge carriers) being present.
9
(i) List two properties of the electron.
Negative charge, negligible mass , orbits nucleus, deflected by electric / magnetic field etc.
(ii) Name the Irishman who gave the electron its name in the nineteenth century.
George Stoney
(iii) Give an expression for the force acting on a charge q moving at a velocity v at right angles to a magnetic
field of flux density B.
F = Bqv
(iv) An electron is emitted from the cathode and accelerated through a potential difference of 4kV in a cathode
ray tube (CRT) as shown in the diagram.
How much energy does the electron gain?
The final kinetic energy gained by the electron equals the initial (electrical) potential energy
= 4 KeV = (4000)(1.6 × 10–19)
=
6.4×10−16 J
(v) What is the speed of the electron at the anode? (Assume that the speed of the electron leaving the cathode is
negligible.)
E = ½ mv2  6.4 ×10-16 = ½ (9.1 × 10-31)(v2)

v =3.75 × 107 m s-1
(vi) After leaving the anode, the electron travels at a constant speed and enters a magnetic field at right angles,
where it is deflected. The flux density of the magnetic field is 5 × 10–2 T.
Calculate the force acting on the electron.
F = Bev = (5 × 10–2)(1.6 × 10–19)( 3.75 × 107)
= 3.0 ×10−13 N
(vii)
Calculate the radius of the circular path followed by the electron, in the
magnetic field.
F = mv2/r
 3.0 ×10−13 = (9.1 × 10–31)( 3.75 × 107)2/r
 r = 4.3×10−3 m
(viii) What happens to the energy of the electron when it hits the screen of the CRT?
It gets converted to light.
10 (a)
(i) Leptons, baryons and mesons belong to the “particle zoo”.
Give (i) an example, (ii) a property, of each of these particles.
LEPTONS; electron, positron, muon , tau, neutrino
Not subject to strong force
BARYONS; proton, neutron
Subject to all forces, three quarks
MESONS pi(on), kaon
Subject to all forces, mass between electron and proton, quark and antiquark
(ii) The following reaction represents pair production.
γ → e + + e–
Calculate the minimum frequency of the γ-ray photon required for this reaction to occur.
E = (2)mc2 = hf
2(9.1 × 10–31)( 3.0 × 108)2 = (6.6 × 10–34)f
 f = 2.5×1020 Hz
(iii) What is the effect on the products of the reaction if the frequency of the γ-ray photon exceeds the minimum
value?
The electrons which were created would move off with greater speed.
There may also be more particles produced.
(iv) The reverse of the above reaction is known as pair annihilation.
Write a reaction that represents pair annihilation.
e+ + e- → 2γ
(v) Explain how the principle of conservation of charge and the principle of conservation of momentum apply
in pair annihilation.
Total charge on both sides is zero
Momentum of positron + electron = momentum of photons
11
Read the following passage and answer the accompanying questions.
Irish Times: Monday, January 11,1999
Radioactive decay helps to determine exact dates.
Radioactive decay occurs with such precision that it is often used as a clock.
Carbon dating has been invaluable to archaeologists, historians and anthropologists.
The method is based on the measurement of 14C, a radioactive isotope of carbon with a half-life of 5730 years. 14C
occurs to a small extent in the atmosphere together with the much more common 12C.
Living organisms constantly exchange carbon with the atmosphere and the ratio of 14C to 12C in living tissue is the
same as it is in the atmosphere.
This ratio is assumed to have remained the same since prehistoric times.
When an organism dies, it stops exchanging carbon with the atmosphere, and its 14C nuclei keep disintegrating while
the 12C in the dead tissue remains undisturbed.
(a) What is radioactive decay?
Radioactivity is the breakup of unstable nuclei with the emission of one or more types of radiation.
(b) What is an isotope?
Isotopes are atoms which have the same Atomic Number but different Mass Numbers.
(c) Apart from “carbon dating”, give two other uses of radioactive isotopes.
Medical imaging, (battery of) heart pacemakers, sterilization, tracers, irradiation of food, killing cancer cells, measuring
thickness, smoke detectors, nuclear fuel
(d) How many neutrons are in a 14C nucleus?
Eight
(e) 14C decays to 14N. Write an equation to represent this nuclear reaction.
14
14
0
6C → 7 N + -1 e
14
(f) How much of a C sample remains after 11 460 years?
11,460 corresponds to two half lives, and after two half lives one quarter remains.
(g) Calculate the decay constant of 14C.
T1/2 = ln 2 /λ
 λ = 0.693/5730
= 1.21 × 10−4 y-1
= 3.8×10−12 s-1
(h) Why does the 12C in dead tissue remain “undisturbed”?
It is not radioactive, it is not exchanging with the atmosphere, it is stable
12 (a)
(i) State Newton’s second law of motion.
Newton’s Second Law of Motion states that the rate of change of an object’s momentum is directly proportional to
the force which caused it, and takes place in the direction of the force.
(ii) A skydiver falls from an aircraft that is flying horizontally. He reaches a constant speed of 50 m s–1 after
falling through a height of 1500 m. Calculate the average vertical acceleration of the skydiver.
v 2= u2+2as
a)(1500)
 a = 0.83 m s-2
(iii) If the mass of the skydiver is 90 kg, what is the magnitude and direction of the average resultant force
acting on him?
F = ma = 90 × 0.83 = 75 N Down
(iv) Use a diagram to show the forces acting on the skydiver and explain why he reaches a constant speed.
Weight acting down on diagram
Air resistance / friction / buoyancy acting up on diagram
Air resistance = weight, therefore resultant force = 0
Therefore acceleration = 0
12 (b)
(i) What is the difference between heat and temperature?
Heat is a form of energy, temperature is a measure of hotness.
(ii) The emf of a thermocouple can be used as a thermometric property. Explain the underlined terms.
An emf is a voltage applied to a full circuit.
A thermometric property is any property which changes measurably with temperature.
(iii) Name a thermometric property other than emf.
Length, pressure, volume, resistance, colour
(iv) Explain why it is necessary to have a standard thermometer.
Two different types of thermometer will give slightly different readings at the same temperature
12 (c)
(i) State Coulomb’s law of force between electric charges.
Coulomb’s Law states that the force between two point charges is proportional to the product of the charges and
inversely proportional to the square of the distance between them.
(ii) Define electric field strength and give its unit.
Electric field strength at a point is the force per unit charge at that point.
The unit of electric field strength is the Newton per Coulomb (NC-1).
(iii) How would you demonstrate an electric field pattern?
Oil and semolina or seeds
High tension / high voltage
Lines of semolina show field
(iv) The diagram shows a negative charge – Q at a point X.
Copy the diagram and show on it the direction of the electric field strength at Y.
Arrow towards X
12 (d)
(i) State the laws of electromagnetic induction.
Faraday’s Law states that the size of the induced emf is proportional to the rate of change of flux.
Lenz’s Law states that the direction of the induced emf is always such as to oppose the change producing it.
(ii) A small magnet is attached to a spring as shown in the diagram. The magnet is set oscillating up and down.
Describe the current flowing in the circuit.
Alternating current.
(iii) If the switch at A is open, the magnet will take longer to come to rest. Explain why.
There is no longer a full circuit, so even though there is an induced potential difference there is
no (induced) current, therefore no induced magnetic field in the coil therefore no opposing force.